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Interaction of Mechanics and Mathematics

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

A Geometric Approach to Modeling and Analysis

Authors: Lee, Taeyoung, Leok, Melvin, McClamroch, N. Harris

  • Accessible to a broad audience of scientists and engineers
  • Non-trivial applications worked out in detail, allowing reader to easily apply techniques to real-world problems
  • Includes exercises at the end of every chapter
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Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-56953-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-319-56951-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities.

The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems.

This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

Table of contents (10 chapters)

  • Mathematical Background

    Lee, Taeyoung (et al.)

    Pages 1-51

  • Kinematics

    Lee, Taeyoung (et al.)

    Pages 53-88

  • Classical Lagrangian and Hamiltonian Dynamics

    Lee, Taeyoung (et al.)

    Pages 89-129

  • Lagrangian and Hamiltonian Dynamics on $$(\mathsf{S}^{1})^{n}$$

    Lee, Taeyoung (et al.)

    Pages 131-206

  • Lagrangian and Hamiltonian Dynamics on $$(\mathsf{S}^{2})^{n}$$

    Lee, Taeyoung (et al.)

    Pages 207-271

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-56953-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-319-56951-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds
Book Subtitle
A Geometric Approach to Modeling and Analysis
Authors
Series Title
Interaction of Mechanics and Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-56953-6
DOI
10.1007/978-3-319-56953-6
Softcover ISBN
978-3-319-56951-2
Series ISSN
1860-6245
Edition Number
1
Number of Pages
XXVII, 539
Number of Illustrations and Tables
49 b/w illustrations
Topics